A class of inertial sensors based on atom interferometry use pulses of light to split, and later, recombine the quantum wavefunctions or wavefunction from a sample of cold thermal or quantum degenerate atoms (Bose-Einstein condensate). While split, the phases of the separate parts evolve independently, allowing the accumulation of a phase difference due to the presence of acceleration and/or rotation. When recombined, this phase difference is manifested by changes in the final quantum momentum state or internal state of each atom, or in the quantum degenerate atom cloud as a whole.
For example, one sensor scheme results in changes to the relative populations of two internal states of the atoms. These populations can be detected by, for example, shining resonant light on the atoms and detecting the scattered fluorescence. The relative populations of the two internal states vary sinusoidally as a function of the phase difference induced by inertial forces. The derivative of the relative population with respect to phase difference is approximated by acquiring population measurements at two different phases. At a peak in the relative population sinusoid, the derivative curve crosses zero. Near the zero crossing of the derivative, a small change in phase will induce a large change in the derivative signal. Near a peak of the derivative, however, a small change in phase will induce only a very small change in derivative signal. It is therefore desirable to operate the atomic inertial sensor near a zero crossing or null point of the derivative signal, where sensitivity is maximized.
There are many examples of sensors that are operated near a null point, in order to maximize sensitivity. A common technique to maintain operation near a null point is to provide closed loop feedback. In this technique, the sensor output is compared to zero, or some other desired operating point. The difference between an open loop output and a setpoint is the error signal. The error signal is fed back to a mechanism on the sensor that forces the sensor to shift its output closer to the setpoint.